is the topological boundary. The set \(E^{(1)}\)  is the Lebesgue set of \(E\)  and \(|E^{(1)}\Delta E|=0.\)  We denote by \(\partial ^*E\)  the reduced boundary of a finite perimeter set \(E\)  [1]}, [2]}, i.e.,
\(\partial ^*E:=\Big \lbrace x\in \mathbb {R}^2:\,\, \exists \nu _E(x):=-\lim \limits _{r\rightarrow 0}\frac{D\chi _E(B_r(x))}{|D\chi _E|(B_r(x))},\quad |\nu _E(x)|=1\Big \rbrace .\) 
